The Analytical Solutions of the Sharma Tasso Olver-Burgers Equation Using Improved Sub-Equation Method

In this study, various traveling wave solutions of the Sharma Tasso Olver-Burgers equation were obtained using the improved sub-equation method in order to achieve traveling wave solutions of nonlinear evolution equations. The Sharma Tasso Olver-Burgers equation, derived from the combination of the Burgers equation and the Sharma Tasso Olver equation, is a solvable model that examines the interaction between nonlinear convection and diffusion processes. This equation is an important tool for describing soliton, shock, and complex wave structures that occur in fields such as fluid mechanics, plasma physics, nonlinear optics, and quantum field theory. In the study, the improved sub-equation method, which is an extended form of the classical sub-equation method, was used; through this method, not only positive power terms but also inverse power components were included in the solution space. Within this framework, sixteen different traveling wave solutions based on hyperbolic and trigonometric functions such as tanh, coth, tan, and cot were obtained. The obtained solutions represent different physical behaviors, such as kink-type solitons, periodic waves, complex structures containing singularities, and rational waves, depending on the system parameters. As a result of graphical analyses, it was determined that the characteristics of the solutions, such as amplitude, velocity, and frequency, are directly related to the system parameters. In three-dimensional (3-D), two-dimensional (2-D), and contour plots, it was observed that the wave profiles exhibit significant energy concentrations in resonance regions. This provides important information for modeling sudden distortions, energy accumulation, and resonance processes in fields such as optics, fluid mechanics, and plasma physics. The developed solutions expanded the solution space of the Sharma Tasso Olver-Burgers equation, and the method has emerged as a powerful, systematic, and generalizable tool for the analytical investigation of nonlinear systems.